Threaded tubular element for fatigue resistant threaded tubular joint and resulting threaded tubular joint

ABSTRACT

The threading of a threaded tubular element comprises at least one tangential multiple radius junction zone ( 21 ) at the thread root, in particular on the load flank side ( 13 ).  
     This zone ( 21 ) comprises a principal arc ( 23 ) with a radius (r P1 ) where the support circle cuts the flank ( 13 ) at a point (P RF1 ). The tangent at (P RF1 ) to this circle makes a strictly positive angle (D) with the flank ( 13 ).  
     The secondary arcs ( 25, 27 ) with radii (r S1  and r T1 ) which are lower than (r P1 ) effect the tangential junction of the principal arc on one side to the flank ( 13 ) and on the other side to the thread root ( 19 ).  
     Radius (r P1 ) is larger than that (r H1 ) of the standard circle ( 29 ) which passes through (P RF1 ) and which would alone constitute a tangential junction zone.  
     Such a threaded element provides a threaded tubular connection which incorporates good resistance to both static and cyclic stresses.

[0001] The present invention relates to a male or female threadedtubular element of a threaded tubular connection which is particularlyable to resist both static and cyclic stresses.

[0002] The present invention also relates to a threaded tubularconnection which is particularly suitable for resisting both static andcyclic stresses.

[0003] Threaded tubular connections comprise a male threaded element atthe end of a first pipe and a female threaded element at the end of asecond pipe which may be a great length pipe or a coupling. Suchthreaded connections are used in particular to constitute casing stringsor production strings or drillpipe strings for hydrocarbon wells or forsimilar wells such as for example geothermal wells.

[0004] In its API specification 5B, the American Petroleum Institute(API) defines threaded connections between casing pipes or betweenproduction pipes in particular with tapered threadings with trapezoidalor round triangular threads.

[0005] Other types of threaded connections are also known which usestraight or tapered two-step threads: see, for example, U.S. Pat No.4,521,042.

[0006] Until recently, casing pipes or production pipes had essentiallyto be capable of resisting different combinations of static stresses(tension, axial compression, plane bending, internal or externalpressure) despite their limited thickness resulting from the need to beable to exploit a deep well and insert a variety of columns of differentdiameters one into another.

[0007] In contrast, drillpipes, which are only used to drill wells, aresubjected to substantial cyclic stresses but are not subjected to sizelimitations, since a single string of a given diameter is downhole at agiven time.

[0008] If not strictly limited, cyclic stresses lead during operation tofatigue ruptures which start at the root of the threads, generally onthe side of the load flanks which are under load.

[0009] This preferred location for initiation of fatigue cracks resultsfrom a stress concentration at the junction between the load flank andthe thread root.

[0010] To improve the resistance to cyclic stresses, it is necessary toreduce the maximum level of the stresses by reducing the general levelof stresses on the load flank and by producing the least possibleangularity of the junction between the load flank and the thread root.

[0011] API specification 7D defines drillpipes with robust taperedthreads which are adapted to operational stresses. API specification 7Dthreads are triangular in shape and very rounded with load and stabbingflanks which are each disposed at 30° with respect to the normal to theaxis of the threaded element.

[0012] The load flank is that which is disposed on each thread on theside opposite the free end of the element. This definition will be usedthroughout the present document.

[0013] The thread root is rounded in an arc of a circle with a radius of0.97 mm (0.038″) centred on the axis of the thread root; this arc of acircle joins tangentially with the flanks.

[0014] The angle of 60° between the thread flanks resulting from thetriangular shape of the threads enables the radius of the arc of acircle to be substantial.

[0015] The thread crests are truncated so as to avoid any radialinterference between the thread crests and the thread roots of the matedthreading.

[0016] The height of the truncated threads is 3.08 mm (0.121″) whichcorresponds to twice the height of API 5B threaded connections.

[0017] These means can, however, prove to be insufficient since U.S.Pat. No. 4,549,754 describes a threading profile which is modified withrespect to API specification 7D for drillpipes which renders it capableof further reducing stress concentration.

[0018] The thread of U.S. Pat. No. 4,549,754 shows in cross section aroot which is not symmetrical but comprises a rounded zone the centre ofwhich is offset towards the stabbing flank (opposite the load flank) andwith the radius increased by about 50% with respect to the API radius,namely 1.45 mm (0.057″).

[0019] This rounded zone joins the load flank tangentially while itjoins with the stabbing flank in a less critical profile: a simplestraight segment or a radius of 0.81 mm (0.032″) followed by a straightsegment.

[0020] The thread root is thus more undercut than an API thread andhence requires a large starting pipe thickness in order to cut thethreads.

[0021] Such a disposition cannot be envisaged for strings of pipes forexploiting wells since these are subjected to both static and dynamicstresses.

[0022] Such demands on stress resistance are now being encountered inunderwater strings connecting the sea bed to offshore hydrocarbonexploitation platforms.

[0023] Such columns of pipes, known to the English-speaking skilledpersons as “risers”, are subjected to cyclic stresses caused inparticular by currents which induce vibrations in the column, by waves,by tides and by possible displacement of the platforms themselves.

[0024] Such demands on stress resistance are also encountered in onshorewells, in particular when dropping rotating pipes in order to cementwells in the very frequent case of wells which deviate from the verticaland have bends.

[0025] For this reason, improvements to threaded tubular connections forcasing pipes, for production pipes or for “risers” have been sought inorder to increase their fatigue strength.

[0026] Patent application WO 98/50 720 describes such an improvedthreaded tubular connection.

[0027] The threadings described in that document have trapezoidalthreads derived from the threads of API specification 5B known as“buttress” threads.

[0028] The trapezoidal shape of the threads limits the risk ofdeformation of the threaded elements which can lead to them dislodgingduring coupling, in particular by overtorquing.

[0029] The thread roots are substantially rectilinear and join to eachof the flanks via a rounded zone the radius of which is comprisedbetween 10% and 50% of the total width of the thread root (andpreferably between 16% and 26% of that total width), the rounded zoneterminating tangentially to the flank and to the thread root.

[0030] The thread heights are such that radial interference between theroot of one thread and the crest of the corresponding thread of themated threading is completely avoided by maintaining a radial clearanceof at least 0.25 mm (0.010″).

[0031] Taking into account the threadings given in the example, theradii at the thread root are of the order of 0.5 mm as opposed to 0.15mm for the radii specified in API 5B.

[0032] Such radii may appear low if they are compared with those ofdrillpipes but the trapezoidal form of the threads used does not allowas large radii to be formed as in the case of triangular threads unlessit is acceptable to drastically reduce the bearing surface of thecontacting flanks.

[0033] The threadings of document WO 98/50720 are also not adapted tointerfering type threads which have a radial interference between thethread crests of one threading and the corresponding thread roots of themated threading. The threads shown are “wedge” type threads with avariable width, like those shown in U.S. Re No. 30 647.

[0034] The aim of the present invention is to produce a male or femalethreaded tubular element for threaded tubular connections, which areparticularly resistant both to:

[0035] a) static stresses, in particular axial tension, axialcompression, bending, torsion, internal or external pressure, dislodgingduring connection, either simple or combined (for exampletension+internal pressure);

[0036] b) cyclic stresses.

[0037] In the remainder of the present document, such a threaded elementwill be described as having an anti-fatigue profile.

[0038] The present invention also aims to ensure that the threadedtubular element of the invention can be formed with all types ofthreadings: tapered, straight, straight-tapered combinations, with oneor more steps, with trapezoidal or triangular threads, which may beinterfering or non-interfering; non interfering threadings are, forexample, of the type described in European patent application EP 0 454147 with simultaneous contact of the two flanks with those of the matedthread (also called “rugged thread”), with an axial interference fit, orof the wedge type with a varying width as described, for example, inU.S. Re 30 647.

[0039] A further aim is that the threaded element can be produced andinspected easily.

[0040] The threaded element of the invention must be able to be used toconstitute threaded connections for strings of hydrocarbon productionpipes, for well casings or for underwater exploitation (“risers”) or forsimilar uses.

[0041] A still further aim is to produce threaded tubular connectionswhich are sealed, in particular gas tight, even under cyclic stresses.

[0042] In a variation, the threaded element of the invention must beable to be used in drillpipe strings.

[0043] A still further aim is to produce a threaded tubular connectionin which only one of the threaded elements, for example the femaleelement, has been modified to resist cyclic stresses but which iscompatible with a non modified mated threaded element.

[0044] In a variation, both threaded elements of the threaded tubularconnection have been modified to resist cyclic stresses.

[0045] In accordance with the invention, the male or female threadedtubular element with an anti-fatigue profile is formed at the end of apipe and comprises an external male or internal female threadingdepending on whether the threaded element is male or female in type.

[0046] The threads comprise a thread crest, a thread root, a rectilinearload flank, a rectilinear stabbing flank and two tangential junctionzones termed “thread root” zones.

[0047] Each of the two tangential thread root junction zones is disposedbetween the thread root and one of the two thread flanks, termed the“corresponding flank”, and comprises an arc of a circle.

[0048] At least one of the two tangential thread root junction zones,termed the “multiple radius zone”, comprises an arc of a circle termedthe “principal arc”, wherein the support circle cuts the supportstraight line of the corresponding flank at a point termed the “flankreference point”, and also a regular curve termed the “secondary curve”either side of the principal arc which tangentially joins this to thecorresponding flank and to the thread root: a non tangential junctionwould introduce a stress peak which is particularly deleterious tofatigue at the singular junction point.

[0049] Similarly, the second curve must be regular, i.e., must not havea singular point which could introduce a stress peak at this location.

[0050] At the flank reference point, the tangent to the support circleof the principal arc makes a strictly positive acute angle with thesupport straight line of the corresponding flank.

[0051] In the remainder of the document, the positive sense is such thatthe principal arc does not undercut the material of the threads: anegative angle between the tangent and flank would clearly beparticularly deleterious for the fatigue behaviour.

[0052] Said support circle of the principal arc cuts or is tangential tothe support straight line of the thread root and the tangent to saidsupport circle makes, at the point of intersection or at the tangentialpoint under consideration, an angle comprised between −15° and +15° withthe support straight line of the thread root.

[0053] When the circle support of the principal arc is tangential to thesupport straight line of the thread root, this angle is zero and thesecondary curve on the thread root side reduces to a point.

[0054] When the thread root reduces to a point, by convention thesupport straight line of the thread root is the straight line passingthrough the thread root which is parallel to the axis of the threadedelement.

[0055] The shape and disposition of the principal arc in any multipleradius zone is perfectly defined:

[0056] by the position of the flank reference point;

[0057] by the angle between the tangent to the circle support of theprincipal arc and the corresponding flank;

[0058] and by the angle between the tangent to said circle and thethread root.

[0059] The radius of the principal arc of each multiple radius zone ofthe thread root is larger than that of the arc of the circle termed the“standard arc” passing through said flank reference point which would byitself constitute a tangential junction zone between the correspondingflank and the thread root.

[0060] The invention can thus use a high junction radius in the criticalzones located towards the middle of the junction zone where theprincipal arc is located and lower radii at the junction with thecorresponding flank and with the thread root where the secondary curvesare located, without consuming too much of the thread height.

[0061] For a given thread height, the closer the flank reference pointto the thread root, the more flank surface is available to bear on thecorresponding surface of the mated threaded element, increasing thestatic performance of the resulting threaded connection.

[0062] In the case of prior art threaded elements, the radial height ofthe junction zone (distance of the flank reference point from the threadroot) is proportional to the radius of this zone. As a result, for thesethreaded elements and for a given thread height, any gain in the fatiguecharacteristics (cyclic stresses) results in weakening the staticcharacteristics.

[0063] In the case of the present invention, because of the positiveangle between the tangent to the support circle of the principal arc andthe flank, the radial height of the unction zone is proportional to theradius of the principal arc but the coefficient of proportionality isall the more lower as this positive angle increases. Thus either thefatigue behaviour under static conditions is improved or the staticconditions for a given fatigue behaviour or the fatigue behaviour andthe static characteristics are improved simultaneously.

[0064] Preferably, the angle between the tangent to the support circleof the principal arc of the multiple radius zone under consideration andthe corresponding flank at the flank reference point is in the range+10° to (70°-J), J designates the corresponding flank angle, i.e., theangle between the rectilinear portion of the flank under considerationand the normal to the axis of the threaded tubular element. The flankangle is said to be positive when the flank under consideration tendsnot to overhang the thread root.

[0065] Highly preferably, the angle between the tangent to the supportcircle of the principal arc of the multiple radius zone underconsideration and the load flank at the flank reference point is in therange +15° to (45°-J), J having the same meaning as above.

[0066] A configuration with a positive or zero flank angle is preferablefrom the point of view of concentrating stresses at the thread roots.

[0067] Preferably, the radius of the principal arc of the multipleradius zone is in the range 150% to 250% of that of the standard arcwhich would constitute a tangential junction zone passing via the flankreference point.

[0068] Preferably again, each secondary curve of the multiple radiuszone is an arc of a circle.

[0069] Highly preferably, the ratio of the radius of the arc of eachsecondary curve to that of the principal arc is in the range 0.1 to 0.4.

[0070] The minimum value of this ratio avoids an excessive increase instresses at the secondary curves.

[0071] The maximum value of this ratio limits the overall extent of themultiple radius zone.

[0072] The invention can be applied by modifying the profile of thethreads either on the side of a single flank, in particular the loadflank which is generally the most loaded, or on the two flanks.

[0073] It can also be applied both to triangular and to trapezoidalthreads with a fixed or varied width and for tapered, straight,combined, simple or multiple-step threadings.

[0074] A variety of embodiments will be described below, in anon-limiting way, which illustrate the scope of the invention.

[0075] The invention also provides a threaded tubular connection with ahigh resistance to static or cyclic stresses, comprising a male threadedtubular element at the end of a first pipe connected by screwing to afemale threaded tubular element at the end of a second pipe by means ofa male threading on the male threaded tubular element and a femalethreading on the female threaded tubular element.

[0076] The term “pipe” means both a great length pipe and a short pipesuch as a coupling.

[0077] The threads of each of the threadings comprise a thread crest, athread root, a rectilinear load flank, a rectilinear stabbing flank andfour junction zones each comprising an arc of a circle.

[0078] Of these four zones, two zones, termed tangential thread rootjunction zones, each join the thread root to a flank termed thecorresponding flank and two zones, termed thread crest junction zones,each join the thread crest to a flank.

[0079] The profile and disposition of each thread crest junction zoneare adapted so as not to interfere with the tangential thread rootjunction zone of the mated threaded element.

[0080] At least one of the two threaded elements, male and female, is athreaded tubular element with an anti-fatigue profile of the presentinvention.

[0081] Preferably in a variation, at least one thread crest junctionzone of a threaded tubular element opposite a tangential thread rootjunction zone with multiple radii of a mated threaded tubular elementwith an anti-fatigue profile is a zone termed a follower which comprisestwo arcs of a circle which join tangentially to each other namely aprincipal arc and a secondary arc, this latter producing the tangentialthread crest junction to the corresponding flank.

[0082] Further, at the point termed the “high junction” of thecorresponding flank where the support circle of the principal arc of thefollowing zone cuts the support straight line of the correspondingflank, the tangent to said circle makes a strictly negative acute anglewith the support straight line of the flank under consideration.

[0083] Under the convention indicated above, such a sign means that theprincipal arc of the thread crest bites into the material of the thread.

[0084] Such a disposition enables the surface area of the flanks incontact to be increased for a given thread height.

[0085] In an advantageous variation from the cost viewpoint, only one ofthe threaded elements, male or female, is of the anti-fatigue type ofthe invention and is compatible with the other threaded element which isa prior art threaded element.

[0086] In an advantageous variation from the viewpoint of maximisingperformance, the two threaded elements, male and female, are of theanti-fatigue type of the invention.

[0087] In a variation, the threaded tubular connection of the inventionis applicable to interference type threadings in which the thread crestof one threading radially interferes with the thread root of the matedthreading.

[0088] In a further variation, the threaded tubular connection of theinvention is applicable to threadings in which the two flanks of eachthread are in contact, with or without contact pressure, with the twoflanks of the mated threading thread, over at least a portion of thelength of the threading: the invention is thus applicable to threadsknown as “rugged threads” with an axial interference fit or with a wedgeof varying height.

[0089] Other advantages and characteristics of the invention will becomeclear from the detailed description below and from the accompanyingdrawings, which not only serve to clarify comprehension of the inventionbut also contribute to the definition thereof, as appropriate.

[0090] All of the figures described below pertain to longitudinalcross-sections passing through the axis of the element or of thethreaded connection.

[0091]FIG. 1 shows a threaded and coupled connection between two pipesusing tapered threadings.

[0092]FIG. 2 shows a threaded connection termed “integral” connectionbetween two pipes using straight, two-step threadings.

[0093]FIG. 3A shows a few trapezoidal threads of a prior art femalethreaded element.

[0094]FIGS. 3B, 3C, 3D and 3E show the junction zones between the facesof the threads of FIG. 3A.

[0095]FIG. 4A shows a few trapezoidal threads of a male threaded elementof the invention.

[0096]FIGS. 4B, 4C, 4D and 4E show the junction zones between the facesof the threads of FIG. 4A.

[0097]FIGS. 4F and 4G each show a detail of FIG. 4B.

[0098]FIG. 5A shows a few trapezoidal threads of a threaded connectionof the invention constituted by connecting the threaded elements ofFIGS. 3A and 4A.

[0099]FIG. 5B shows a detail of the connection of FIG. 5A at thejunction zones of FIGS. 3C and 4B.

[0100]FIG. 6A shows a few trapezoidal threads of a variation of a femalethreaded element of the invention.

[0101]FIGS. 6B, 6C, 6D and 6E show the junction zones between the facesof the threads of FIG. 6A.

[0102]FIG. 7A shows a few trapezoidal threads of a variation of a malethreaded element of the invention.

[0103]FIGS. 7B, 7C, 7D and 7E show the junction zones between the facesof the threads of FIG. 7A.

[0104]FIG. 8A shows a few trapezoidal threads of a variation of athreaded connection of the invention constituted by connecting thethreaded elements of FIGS. 6A and 7A.

[0105]FIG. 8B shows a detail of the connection of FIG. 8A at thejunction zones of FIGS. 6C and 7B.

[0106]FIG. 8C shows a detail of the connection of FIG. 8A at thejunction zones of FIGS. 6B and 7C.

[0107]FIG. 9A shows a few triangular threads of a further variation of afemale threaded element of the invention.

[0108]FIGS. 9B and 9C show the junction zones between the thread flanksof FIG. 9A.

[0109]FIG. 10A shows a few triangular threads of a further variation ofa male threaded element of the invention.

[0110]FIGS. 10B and 10C show the junction zones between the threadflanks of FIG. 10A.

[0111]FIG. 11A shows a few threads of a further variation of a threadedconnection of the invention constituted by connecting the threadedelements of FIGS. 9A and 10A.

[0112]FIG. 11B shows a detail of the connection of FIG. 11A at thejunction zones of FIGS. 9C and 10B.

[0113]FIG. 11C shows a detail of the connection of FIG. 11A at thejunction zones of FIGS. 9B and 10C.

[0114]FIG. 12 is a graph showing the variation of the ratio of theradius of the principal arc to that of the standard circle of a junctionzone as a function of the angle at the flank reference point fordifferent values of the angle at the thread root junction point.

[0115]FIG. 13 shows the same graph for different values of the loadflank angle.

[0116]FIG. 14 is a graph showing the variation in the principal stressas a function of the angular position on the junction zone between thethread root and the load flank of a threaded tubular connectionsubjected to the internal pressure of a fluid.

[0117]FIG. 1 shows a threaded and coupled connection 200 between twogreat length pipes 101, 101′.

[0118] The term “great length” means pipes several meters in length, forexample about 10 m long.

[0119] Such pipes are routinely connected to constitute strings ofcasing pipes or production pipes or “risers” for onshore or offshorehydrocarbon wells or for strings of drillpipes for the same wells.

[0120] The pipes can be formed from all types of non alloy steels, lightalloy steels or high alloy steels, or from ferrous or non ferrous alloysto adapt them to different operational conditions: the level ofmechanical stress or the corrosive nature of the fluid internal orexternal to the pipes.

[0121] It is also possible to use low corrosion resistance pipesprovided with a coating, for example of synthetic material preventingany contact between the steel and the corrosive fluid.

[0122] Pipes 101, 101′ comprise at their ends identical male threadedelements 1, 1′ and are connected via a coupling 202 comprising a femalethreaded element 2, 2′ at each end.

[0123] Male threaded elements 1, 1′ are respectively connected byscrewing into the female threaded elements 2, 2′ to constitute twosymmetrical threaded connections 100, 100′ which are joined by aprojection 10 a few centimeters long.

[0124] The internal diameter of projection 10 of the coupling issubstantially identical to that of pipes 101, 101′ such that the flow offluid circulating internally is not perturbed.

[0125] Since threaded connections 100, 100′ are symmetrical, only one ofthese connections will be described.

[0126] In FIG. 1, the threadings are shown diagrammatically bygeneratrices or envelopes of the thread crest and thread root.

[0127] Male threaded element 1 comprises a male threading 3 inaccordance with API specification 5B, tapered as the case may be withtriangular or trapezoidal threads and disposed on the outside of themale element. Male threading 3 is separated from the free end 7 of saidelement by a non-threaded lip 11. The free end 7 is a substantiallytransverse annular surface.

[0128] Adjoining free end 7 on the outer surface of lip 11 is a taperedbearing surface 5 the taper of which is greater than that of malethreading 3.

[0129] Female element 2 comprises means which mate with those of maleelement 1, i.e., they correspond in shape and are intended to co-operateas regards their position with the male means.

[0130] Female element 2 thus comprises an internal tapered femalethreading 4 and a non threaded portion between the threading and aprojection 10.

[0131] This non threaded portion comprises a substantially transverseannular orientation surface 8 forming a shoulder at the end of theprojection and a tapered bearing surface 6 following the shoulder.

[0132] Screwing male element 1 into female element 2 makes theconnection.

[0133] Makeup of the male element into the female element is stoppedwhen the transverse surfaces 7 and 8 abut each other. The bearingsurfaces 5, 6 are designed to interfere radially with each other and arethus under metal-metal contact pressure. The bearing surfaces 5, 6 thusconstitute sealing surfaces which make the threaded connection tighteven under high internal or external fluid pressures.

[0134] If a tight seal is not required, projection 10 can be dispensedwith, and therefore the transverse abutting surface 8 and the bearingsurfaces 5, 6.

[0135] In a variation, two great length pipes can be screw connecteddirectly as shown in FIG. 2; this type of connection 300, which usesonly a single threaded connection, is termed integral.

[0136] One end of pipe 301 is provided with a male threaded element 1;the second pipe 302 is provided with a female threaded element 2 at thecorresponding end.

[0137] Male threaded element 1 comprises an external male threadingconstituted in the present case by two straight steps or windings 303,303′ with round triangular or trapezoidal threads separated by atransverse annular shoulder 307, the winding with the lower diameter303′ being disposed at the free end 309′ of the element; the free end309′ being a transverse annular surface.

[0138] A tapered bearing surface 311′ is located on the outside surfacebetween the threaded portion 303′ and the end surface 309′.

[0139] On the opposite side on the male element, the threaded portion303 is extended by a non threaded portion comprising a tapered bearingsurface 311 and a transverse annular surface 309 forming a shoulder.

[0140] The female threaded element 2 comprises internal female meanswhich mate with the male means.

[0141] Thus the female element 2 comprises a female threadingconstituted by two straight windings 304, 304′ separated by a transverseannular shoulder 308, the winding with the largest diameter 304 beingdisposed towards the transverse annular free end 310 of the femaleelement.

[0142] The female element also comprises two tapered bearing surfaces312, 312′ corresponding to the male bearing surfaces 311, 311′ and atransverse annular surface 310′ forming a shoulder at the end of theelement opposite to the free end 310.

[0143] In its made up state, the male threaded portions 303, 303′ arerespectively s screwed into the female threaded elements 304, 304′ andthe central shoulders 307, 308 abut against each other. The transverseend surfaces 309, 309′ are in partial contact with those of theshoulders 310, 310′ respectively and constitute auxiliary abutments forthe principal abutment 307, 308.

[0144] The male bearing surfaces 311, 311′ respectively radiallyinterfere with the female bearing surfaces 312, 312′ and develop highmetal-metal contact pressures which can seal the connection againstexternal or internal fluids.

[0145] In variations which are not shown, the threaded and coupledconnection can have straight threadings and the integral connection canhave tapered threadings.

[0146] The threadings can also each have two tapered threaded portionswith a different taper or can be straight-tapered, and the threadedportions of the same threading may or may not be stepped.

[0147] The next figures describe variations of threads of threadedtubular elements for a threaded tubular connection which can resist bothstatic and cyclic stresses.

[0148]FIG. 3A shows a thread 12 of a tapered female internal threading 4of a female threaded tubular element 2 of FIG. 1.

[0149] Female threads 12 are trapezoidal in shape and comprise fourrectilinear faces, namely a thread crest 20, a thread root 18 and twoflanks: a load flank 14 and a stabbing flank 16.

[0150] In the case shown, the thread crests and roots are inclined at anangle C with respect to the axis of the threaded element: angle C is thetaper angle of the threading; the thread height is constant for eachflank.

[0151] Alternatively, it is possible to have a tapered threading withthread crests and roots which are disposed parallel to the axis of thethreaded element: the thread height is then higher on the stabbing flankside than on the load flank side for the threading to be tapered.

[0152] Stabbing flank 16 is the flank which comes into contact firstwith the corresponding flank on the mated threading when the male andfemale elements are engaged one in the other: it is located on thethread on the side of the free end of the threaded element.

[0153] Load flank 14 is thus disposed on the side opposite the free endof the threaded element.

[0154] Load flank 14 makes an angle A with the normal to the axis of thethreaded element and the stabbing flank makes an angle B with the samenormal.

[0155] Angles A and B are defined as positive by convention in that thecorresponding flanks 14 and 16 do not overhang the thread root 18.

[0156] The flanks are joined to the thread crest and root by fourtangential junction zones 22, 32, 42, 52 each constituted by a simplearc of a circle as shown in FIGS. 3B, 3C, 3D and 3E.

[0157] Zones 22 and 52 with respective radii r_(2fp) and r_(2fe) aretangential thread root junction zones while zones 32 and 42 with radiir_(2sp) and r_(2se) are thread crest junction zones.

[0158] The term “tangential” for junction zones 22, 32, 42, 52 meansthat the arc of the circle from which these zones are constituted istangential at its ends to the faces it joins. This avoids any angularitywhich can create a stress peak when these zones are placed under stress.

[0159]FIG. 4A represents a thread 11 of a tapered male externalthreading 3 of a male threaded tubular element 1 of FIG. 1.

[0160] As with female element 12, male thread 11 is trapezoidal in shapeand comprises four rectilinear faces, namely a thread crest 17, a threadroot 19 and two flanks: a load flank 13 and a stabbing flank 15.

[0161] The male threads 11 are adapted to be screwed into female threads12. The male thread crests and roots are thus inclined at the same angleC as the female thread crests and roots. The angles A of the load flankand B of the stabbing flank of the male thread 11 are identical to thoseof female thread 12.

[0162] The flanks are joined to the thread crest and the thread root viafour tangential junction zones 21, 31, 41, 51.

[0163] The tangential junction zones for the thread crest 31, 41 and thethread root 51 are constituted by a simple arc of a circle withrespective radii r_(1sp), r_(1se) and r_(1fe) and are shown in FIGS. 4C,4D and 4E.

[0164] The tangential thread root junction zone 21 disposed between thethread root and load flank is constituted by several consecutive arcs ofa circle with different radii and tangents.

[0165] This zone 21 is shown in detail in FIGS. 4B, 4F and 4G and forthis reason is termed the “multiple radius zone”.

[0166] The multiple radius zone 21 comprises a median portion with anarc of a circle termed the “principal arc” 23 with radius r_(p1) and anarc of a circle termed the “secondary arc” on each side of thisprincipal arc, a first secondary arc 25 on the load flank side 13 withradius r_(s1) and tangential to the load flank and a second secondaryarc 27 on the thread root side 19 with a radius r_(T1) and tangential tothe thread root.

[0167] The support circle of the principal arc 23 cuts the supportstraight line of the load flank 13 at point P_(RF1) termed “flankreference” without being tangential to this support straight line.

[0168] Thus there exists at point P_(RF1) an angle D between the tangent61 to the support circle of the principal arc 23 and the supportstraight line of the load flank 13. This angle D is strictly positiveusing the convention we have employed in which such an angle is positivewhen the principal arc does not cut into the material of the thread;tangent 61 is thus inside thread 11 with respect to the support straightline of the load flank.

[0169] The support circle of the principal arc 23 cuts the supportstraight line of the thread root 19 at point P_(RR1) without being at atangent to this support straight line.

[0170] Tangent 63 to the support circle of the principal arc 23 at pointP_(RR1) thus makes an angle E with the support straight line to thethread root 19 which is slightly positive.

[0171] The inventors have established that for the threaded connectionto function properly, angle E has to be limited to range of +15° to−15°, for example 10°, a negative angle corresponding, using our signconvention, to a principal arc which cuts into the material of thethread or the thread root in the present case.

[0172] Fixing the position of point P_(RF1) on load flank 13 and anglesD and E can thus perfectly define radius r_(P1) of principal arc 23.

[0173] When the taper of the threading is low (angle C being a fewdegrees) and the load flank 13 is substantially normal to the threadroot 19, radius r_(P1) is close to twice radius r_(H1) of thehypothetical circle termed the “standard circle” 29 passing throughpoint P_(RF1) and which would alone constitute a tangential junctionzone between the load flank and the thread root. This means that thestandard circle 29 passing through P_(RF1) is tangential both to thethread root 19 and to the load flank 13.

[0174] The most influential factor on the value of the ratio(r_(P1)/r_(H1)) in the permitted variations is the angle D.

[0175] When angle D is too low, less than 10°, the ratio (r_(P1)/r_(H1))is barely more than 1 and thus has a limited effect on the fatiguebehaviour. As a result, an angle D of more than 10° is selected,preferably more than 15°.

[0176] Too large an angle D can cause a geometric incompatibility in thecase of threads with very positively inclined load flanks. For thisreason the upper limit for D is (70°-A), preferably (45°-A).

[0177] Further, too high an angle D in the case of a highly positiveangle A causes the values of the ratio (r_(P1)/r_(H1)) to be too highwhich necessitates the use of secondary arcs with a low radius which arethe origin of undesirable peaks in operational stress at these arcs 25and 27.

[0178] For this reason, angles D and E are selected with regard toangles A and C such that the ratio (r_(P1)/r_(H1)) is in the range 1.5to 2.5. In the present case, E=10° and D=30°.

[0179] The secondary arcs 25, 27 have respective radii r_(S1), r_(T1)which are lower than r_(P1).

[0180] This does not affect the operational behaviour of the threadingsas the inventors have established that the most stressed portion andthus the most critical portion of the thread root junction zone is themedial portion of the principal arc 23 at the root of the threading onthe load flank side.

[0181] In threaded couplings subjected to tensile loads of large butvarying intensity, fatigue cracks are generally observed to start in themedial portion of the thread root junction zone on the load flank sidewhich supports the tensile loads on the threaded elements.

[0182] Too low a radius for the secondary arc can, however, induce asecondary stress peak at the arcs 25 or 27 which can in the secondinstance initiate operational fatigue cracks.

[0183] Too high a secondary arc radius, on the other hand, leads to arcs25 or 27 where relatively too large a size especially when radius r_(P1)is large.

[0184] Preferably, the value r_(S1)/r_(P1) is in the range 0.1 to 0.4.

[0185]FIG. 5A shows the male thread 11 of FIG. 4A and the female thread12 of FIG. 3A once the male and female elements 1, 2 are connected byscrewing to constitute a threaded tubular connection of type 100 shownin FIG. 1.

[0186] Threads 11, 12 of FIG. 5A are termed interfering as the threadcrest 20 of one of the threadings, in this instance the femalethreading, radially interferes with the thread root 19 of the matedthreading, the male thread in this case.

[0187] Male and female load flanks 13, 14 are also in contact and aresubjected to axial tensile loads, generated by the weight of the pipesin the string and in the case of the threaded connections of FIG. 1 toforces generated by abutment of the transverse surfaces 7, 8 with amakeup torque of several kN.m.

[0188] It should be noted that similar tensile loads are obtained whenabutting the shoulders 307, 308 of FIG. 2.

[0189] Returning to FIG. 5A, a clearance is provided between the malethread crest 17 and the female thread root 18 and between stabbingflanks 15, 16.

[0190] These clearances also limit the risks of interference between themale and female junction zones such as 31/22, 41/52 and 51/42, even foridentical radii between mated junction zones.

[0191] Radius r_(2sp) of junction zone 32 of the female thread crest onthe load flank side is selected so as to be sufficiently large so as notto interfere with the multiple radius zone 21.

[0192] Any interference between zones 21 and 32 would cause a stresspeak and an unacceptable risk of rupture in operation.

[0193] The use of a multiple radius zone 21 at the male thread root onthe load flank side can increase the radius of the critical portion ofthe most stressed tangential junction zone if a starting point for thetangential junction zone is fixed on the load flank: see the aboveanalysis of the values of the ratio r_(P1)/r_(H1).

[0194] It is also possible to fix a minimum value for the principal arcand analyse the gain in the bearing surface of the thread and thus thestatic characteristics of the threaded connection. It is true that thisgain is partially reduced by using a simple radius r_(2sp) on the matedfemale junction: see FIG. 5B.

[0195] However, it should be noted that taking into account the priorart it is only necessary to modify one single junction zone on oneelement, in this case the male element.

[0196] It is also possible to modify only the female element. It is thenpossible for the user to employ pipes 101 comprising prior art malethreaded elements and to provide only couplings 202 with modified femalethreads comprising a multiple radius zone between the thread root andload flank.

[0197] Finally, it should be emphasised that threads with junction zoneswith multiple radius zones are not more difficult to machine or inspectthan standard prior art threads comprising junction zones with a singleradius: machining is carried out using tools with a suitable form andinspection is carried out conventionally by superimposing two gaugesmachined to the two extremities of the manufacturing tolerances (knownas “overlay inspection”).

[0198]FIG. 6A shows a female thread 12 with a trapezoidal shape globallysimilar to that of FIG. 3A.

[0199] This thread, however, incorporates differences over that of FIG.3A which concern the two load flank side junction zones, namely zone 22of the thread root and zone 32 of the thread crest which are bothmultiple radius zones.

[0200] Zone 22 is shown in detail in FIG. 6B.

[0201] It comprises a principal arc 24 and a secondary arc 26 tangentialon one side to the principal arc and on the other to the load flank 14.The principal arc joins tangentially to the thread root 18 such that itis not necessary to provide a second secondary arc to join at thispoint.

[0202] The principal arc cuts the load flank 14 at point P_(RF2) and thetangent 62 to the support circle of the principal arc 24 at P_(RF2)makes a strictly positive angle D with the support straight line of loadflank 14.

[0203] The same sign convention as described above is used.

[0204] In FIG. 4B, angle D is +30°.

[0205] Because of the positive angle D, radius r_(p2) of principal arc24 is larger than r_(H2) of standard circle 30 alone constituting thetangential junction zone between load flank 14 and thread root 18.

[0206] The value of the ratio r_(p2)/r_(H2) satisfies the sameconsiderations as those described for junction 21 of FIG. 4B, thepresent case constituting a particular case in which angle E is zero.

[0207] The secondary arc 26 has a radius r_(S2) which is lower than thatof the principal arc for the reasons already described in the case ofFIG. 4B.

[0208] Thread crest junction zone 32 is shown in detail in FIG. 6C.

[0209] It comprises a principal arc 34 and a secondary arc 36, thelatter being tangential on one side to the principal arc 34 and on theother side to the load flank 14.

[0210] The support circle of the principal arc 34 cuts the load flank ata point P_(RH2) termed the “high junction point”.

[0211] The tangent 66 at P_(RH2) to the principal arc 34 makes an angleH with the load flank 14.

[0212] Angle H is strictly negative using our sign convention, i.e.principal arc 34 cuts or bites into the material of thread 12.

[0213] The importance of such a configuration for the junction zone 32is that with an identical radius it can locate point P_(RH2) closer tothe thread crest than in the case of a junction such as 42 (see FIG. 6D)constituted by a simple arc of a circle.

[0214] If desired, the junction between the zone 32 and the thread crestcan be tangential in a manner not shown in FIG. 6C, via a secondsecondary arc.

[0215] Moreover the radius r_(P6) of the principal arc 34 can beinfinite if required, arc 34 then becoming a straight line.

[0216] The radius r_(S6) of the secondary arc 36 is always lower thanthe radius r_(P6) of the principal arc 34. This will be the same for afurther secondary arc on the thread crest side.

[0217]FIG. 7A shows a male thread 11 with a globally trapezoidal shapesimilar to that of FIG. 4A.

[0218] This thread is of a shape adapted for makeup into the femalethread 12 of FIG. 6A.

[0219] As for FIG. 6A, the junction zones 41, 51 of the stabbing flankside have a simple radius (see FIG. 6D and 6E) while those of 21 and 31of the load flank have multiple radii.

[0220] Tangential thread crest junction zone (FIG. 7C) is similar tothat 21 of FIG. 4A except that angle E is zero, and there is no need fora secondary arc to join the principal arc 23 to the thread root 19: zone21 thus wholly matches zone 22 of FIG. 6B: in particular, angle D is+30°.

[0221] Thread crest junction zone 31 (FIG. 7B) is similar and matcheszone 32 of FIG. 6C.

[0222]FIG. 8A shows the male thread 11 of FIG. 7A and the female thread12 of FIG. 6A once threaded elements 1, 2 have been connected byscrewing to constitute the threaded tubular connection 100 of FIG. 1.

[0223] Threads 11, 12 of FIG. 8A are of the interfering type as arethose of FIG. 5A: only the female thread crests 20 are in contact undercontact pressure with the male thread roots 19, also the male and femaleload flanks 13, 14.

[0224]FIGS. 8B and 8C show the relative disposition of the connectedmultiple radius junction zones 21, 32, 31, 32. Because of themodification of the thread crest junction, the male and female loadflanks 13, 14 can bear over a larger surface than in the case of FIG. 5Aand can thus support higher static tensile loads.

[0225] Further, the male and female threaded elements have been bothmodified, and the fatigue behaviour of the connection is not limited bythe fatigue behaviour of the unmodified threaded element as is the casewith FIG. 5A.

[0226] In contrast, this type of threaded connection requires theprovision of modified male and female anti-fatigue profile typeelements.

[0227]FIG. 9A shows a female thread 12 with a triangular shape on afemale threaded tubular element of FIG. 1.

[0228] Female thread 12 comprises:

[0229] a thread crest S2;

[0230] a thread root F2;

[0231] a load flank 14 making an angle A with the normal to the axis tothreaded element 2;

[0232] a stabbing flank 16 making an angle B with the normal to the axisof threaded element 2.

[0233] The angles A and B are both 30° as in API specification 5B.

[0234] The definition of the load flank and of the stabbing flank is thesame as that given above.

[0235] Since threading 4 is tapered, the line joining the thread crestsand that joining the thread roots make an angle C with the axis of thethreaded element.

[0236] Flanks 14, 16 are joined to crest S2 and to root F2 of the threadby tangential junction zones 22, 32, 42, 52.

[0237] Zones 32, 42 of the thread crest are symmetrical with respect tothe normal to the axis of the threaded element passing via crest S2;they are constituted by a simple arc of a circle with radius r_(2s): seeFIG. 9C.

[0238] Zones 22, 52 of the thread root are not symmetrical with respectto the normal to the axis of the threaded element passing through rootF2; they are constituted by multiple radii: see FIG. 9B.

[0239] Zone 22 comprises a principal arc 24 with radius r_(p2) which istangential to F2 at the thread root support straight line. The supportcircle for the arc 24 cuts the support straight line of load flank 14 atP_(RF2).

[0240] Using the convention described above, the support straight lineof the thread root in the case of triangular threads is defined as beingthe straight line parallel to the axis of the connection passing throughthread root F2.

[0241] At P_(RF2), the tangent 62 of the principal arc 24 makes apositive angle D with load flank 14. Angle D is 30°, for example.

[0242] Zone 22 also comprises a secondary arc 26 with radius r_(s2) oneend of which is tangential to the end of the principal arc 24 and theother end of which is tangential to the load flank 14.

[0243] The radius r_(p2) of the principal arc 24 is thus larger than theradius r_(H2) of a standard circle with a not drawn tangent at P_(RF2)of the load flank and at F2 to the support straight line of the threadroot and thus induces the anti-fatigue characteristics at the junctionbetween the thread root and load flank.

[0244] The radius r_(S2) is lower than radius r_(P2) and is preferablyin the range 0.1 to 0.4 times r_(p2).

[0245] Zone 52 comprises a principal arc 54 with radius r_(p4) which istangential at F2 to the support straight line of the thread root. Thesupport circle of arc 54 cuts the support straight line of stabbingflank 16 at P_(RF4).

[0246] At P_(RF4), the tangent 68 to the principal arc 24 makes apositive angle F with the stabbing flank 16. Angle F is 15°, forexample.

[0247] Zone 52 also comprises a secondary arc 56 with radius r_(S4) oneend of which is tangential to the end of principal arc 54 and the otherend of which is tangential to stabbing flank 16.

[0248] The radius r_(p4) of the principal arc 54 is thus higher than theradius r_(H4) of a standard circle with a not drawn tangent at P_(RF4)to the stabbing flank 16 and at F2 to the support straight line of thethread root and thus induces the anti-fatigue characteristics of thejunction between the thread root and the load flank.

[0249] Radius r_(S4) is lower than radius r_(p4) and is preferably inthe range 0.1 to 0.4 times r_(p4).

[0250] In this way, the design of the threaded element aims to improvethe fatigue behaviour of the whole thread root when the two flanks 14,16 are subjected to cyclic loads but when the load flank is furtherstressed, which is generally the case with pipe strings operatingalternately in compression or subjected to bending efforts.

[0251]FIG. 10A shows a male thread 11 which can be screwed into thefemale thread 12 of FIG. 9A.

[0252] This male thread 11 comprises a thread crest S1, a thread rootF1, a load flank 13 and a stabbing flank 15.

[0253] Flanks 13, 15 are joined to thread crests S1 and roots F1 byjunction zones 21, 31, 41, 51.

[0254] Zones 31, 41 of the thread crest are shown in FIG. 10B and areconstituted by an arc of a circle with radius r_(1s) and are similar to32, 42 shown in FIG. 9C.

[0255] Thread root zones 21, 51 shown in FIG. 10C are multiple radiuszones; they are similar to 22, 52 shown in FIG. 9B and match them.

[0256]FIG. 11A shows the male thread 11 of FIG. 10A and female thread 12of FIG. 9A connected after screwing to constitute the threaded tubularconnection of FIG. 1.

[0257] Threads 11, 12 are in contact under contact pressure by their twoflanks: male load flank 13 is in contact with female load flank 14 andmale stabbing flank 15 is in contact with female stabbing flank 16.

[0258] In contrast, there is a clearance between the crests and roots ofmated threads (F1/S2 and F2/S1) and between the corresponding junctionzones (21/42, 51/32, 41/52, 31/22): see FIGS. 11B and 11C.

[0259] This clearance and the shape of the threads and the junctionzones with large radius principal arcs at the thread root produce goodtension-compression fatigue behaviour or bending behaviour of this typeof threaded tubular connection with triangular threads.

[0260]FIGS. 12 and 13 illustrate the influence for differentcombinations of angles A and E of angle D on the value of the ratior_(P1)/r_(H1) of the radius of the principal arc of the multiple radiuszone of the thread root to that of the standard arc constituting thetangential junction zone alone.

[0261] It appears from FIGS. 12 and 13 that the ratio r_(P1)/r_(H1)increases with angle D. FIG. 12 shows that the influence of angle E ismodest and is in agreement with the small variations tolerated for thisangle: an angle E of 15° can produce slightly higher values forr_(P1)/r_(H1) than when E=0°.

[0262] For the load flanks of trapezoidal threads which are generallynot much inclined and correspond to (A-C) close to 0°, angle D canadvantageously be selected in the range 15° to 45°, corresponding to thepreferred range claimed for this angle when angle A is zero.

[0263]FIG. 13 shows the influence of angle A: the ratio r_(P1)/r_(H1)increases when angle A increases algebraically.

[0264] A slightly negative angle A (load flanks overhanging the threadstermed “hook threads”) necessitates a relatively high angle D to obtaina substantial gain in r_(P1).

[0265] A very positive angle A limits the value of angle D to 30°, oreven 20°: such values for angle A are encountered with triangularthreads.

[0266] The stabbing flanks of the trapezoidal threads are also generallymore steeply inclined than the load flanks: the influence of angle B canbe directly traced to that of angle A.

[0267]FIG. 14 shows the variation in the principal stress in thejunction zone between the thread root and the load flank in the medialportion of the threading in the following configuration of a threadedconnection for “risers” for the junction between the sea bed and theplatform for offshore oilfield exploitation:

[0268] pipes with external diameters of 339.7 mm (13⅜″) connected withthreaded and coupled connections of the type shown in FIG. 1;

[0269] tapered threadings (⅙ taper, i.e., an angle C of 4.8°);

[0270] 4 threads per inch (thread pitch 6.35 mm);

[0271] trapezoidal threads 2.1 mm high with crests and roots parallel tothe pipe axis;

[0272] straight load flanks (A=0°);

[0273] inclined stabbing flanks (B=15°);

[0274] axial load under tension causing a tensile stress in the pipebodies of 80% of the elastic limit of the material;

[0275] connections made up to abut with a standard makeup torque.

[0276]FIG. 14 compares the calculated value of the principal tensilestress on an elementary cube of material on the surface of a junctionzone between the thread root and the load flank in the case of astandard junction with a single arc with a radius of 0.375 mm (STDcurve) and with a multiple radius junction zone (RM curve).

[0277] The parameters of the multiple radius zone are:

[0278] D=30° E=0°

[0279] R_(p1)=0.64 mm r_(s1)=0.19 mm r_(P1)/r_(s1)=0.3

[0280] Position of point P_(RF1) on load flank=0.32 mm from the supportstraight line of the thread root.

[0281]FIG. 14 shows an elementary cube of material on the surface of thejunction zone at angular position θ and the value of the principaltensile stress σ on the face of the cube normal to the tangent to thesurface of the junction zone as a function of the angular position θ;the position 0° corresponds to the end of the junction zone with thethread root and the position 90° to the other end of the zone on theload flank side.

[0282] A maximum in the principal stress C can be seen in the medialportion of the junction zone and in particular around the angularposition 30°.

[0283] The use of a multiple radius junction zone can slightly reducethe position of the flank reference point to 0.32 mm against 0.375 mmfor a standard junction and by about 20% of the maximum value of theprincipal stress σ.

[0284] Such a reduction causes a considerable gain in the number ofcycles before fatigue rupture of the threaded connections.

[0285] The use of a ratio r_(S1)/r_(P1) of 0.3 can limit the appearanceof the secondary stress peak at the 70° position.

[0286] The present invention is not limited to the embodiments whichhave been described above.

[0287] The invention can in particular be applied to straight threadings(angle C=0) of the type shown at 303, 303′, 304, 304′ used in thethreaded tubular connections 300 of FIG. 2.

[0288] It is also applicable to trapezoidal threads where the two flanksare in contact with or without contact pressure with the two flanks ofthe mated thread.

[0289] This is the case of threads known as rugged threads for threadedconnections designed to operate under tension and compression such asthose described in EP 0 454 147. In that document, the male and femaleload flanks are in contact under contact pressure and the male andfemale stabbing flanks are also in contact over a substantial proportionof the length of the threadings.

[0290] This is also the case with the axial interference fit flanksdescribed in WO 00/14441.

[0291] This is also the case with wedge threads with variable widthdescribed in WO 94/29627.

[0292] The description of the triangular threads with the multipleradius thread root junction zone on each flank can be directly adaptedto such trapezoidal threads, a trapezoidal thread simply being atriangular thread where the crests and roots have been truncated.

[0293] In the case of such trapezoidal threads, it is possible to use atthe thread roots multiple radius zone junction zones with a principalarc radius which is different between the zone relating to the loadflank and the zone relating to the stabbing flank.

[0294] Since this stabbing flank is generally less loaded than the loadflank in trapezoidal threads where the two flanks are in contact withthe corresponding flanks of the mated threaded element, the principalarc r_(p) can advantageously be higher for the junction 21 and/or 22 ofthe load flank side than for that 51 and/or 52 on the stabbing flankside.

[0295] Alternatively, the principal radius r_(p) can be identical forzones 21, 22, 51 and 52.

1. A male or female threaded tubular element (1, 2) for a threadedtubular connection (100, 300) formed at the end of a pipe (101, 102,202, 301, 302) and comprising an external male threading (3, 303, 303′)or an internal female threading (4, 304, 304′) depending on whether thethreaded element is male or female in type, the threads of which (11,12), viewed in longitudinal cross section passing through the axis ofthe threaded element, comprise a thread crest (17, 20, S1, S2), a threadroot (18, 19, F1, F2), a rectilinear load flank (13, 14), a rectilinearstabbing flank (15, 16) and two tangential thread root junction zones(21, 22, 51, 52) each of these two zones being disposed between thethread root and one of the two flanks termed the corresponding flank andcomprising an arc of a circle, characterized in that at least one of thetwo tangential thread root junction zones termed the “multiple radiuszone” comprises an arc of a circle termed the principal arc (23, 24, 53,54) where the support circle cuts the support straight line of thecorresponding flank at a point termed the flank reference point(P_(RF1), P_(RF2), P_(RF3), P_(RF4)), and a regular curve termed thesecondary curve (25, 26, 27, 55, 56) either side of the principal arc,which tangentially joins this to the corresponding flank on one side andto the thread root on the other and in that: a) at the flank referencepoint, the tangent (61, 62, 67, 68) of the support circle of theprincipal arc makes an acute angle (D, F) which is strictly positivewith the support straight line of the corresponding flank, the positivesense being such that the principal arc does not cut into the materialof the thread flank; b) said support circle of the principal arc cuts oris tangential to the support straight line of the thread root, thetangent to said support circle (63) making, at the intersection point(P_(RR1) or at the tangent point under consideration, an angle (E) inthe range −15° to +15° with the support straight line of the threadroot.
 2. A threaded tubular element according to claim 1, characterizedin that at the flank reference point of the multiple radius zone underconsideration, the angle (D, F) between the tangent to the supportcircle of the principal arc and the corresponding flank is comprisedbetween 10° and the difference (70°-J) if J is the algebraic angle (A,B) between the corresponding flank and a normal to the axis of thethreaded element.
 3. A threaded tubular element according to claim 2,characterized in that at the flank reference point of the multipleradius zone under consideration, the angle (D, F) between the tangent tothe support circle of the principal arc and the corresponding flank iscomprised between 15° and the difference (45°-J) if J is the algebraicangle (A, B) between the corresponding flank and a normal to the axis ofthe threaded element.
 4. A threaded tubular element according to any oneof claims 1 to 3, characterized in that the radius (r_(P1), r_(P2)) ofthe principal arc (23, 24) of the multiple radius zone is comprisedbetween 150% and 250% of that (r_(H1), r_(H2)) of the standard arc (29,30) passing through the flank reference point which would aloneconstitute a tangential junction zone between the corresponding flankand the thread root.
 5. A threaded tubular element according to any oneof claims 1 to 4, characterized in that each secondary curve (25, 26,27, 55, 56) of the multiple radius zone is an arc of a circle.
 6. Athreaded tubular element according to claim 5, characterized in that theratio of the radius (r_(S1), r_(S2), r_(S3), r_(S4), r_(T1)) of the arcof each secondary curve (25, 26, 27, 55, 56) to that (r_(P1), r_(P2),r_(P3), r_(P4)) of the principal arc of a multiple radius zone is in therange 0.1 to 0.4.
 7. A threaded tubular element according to any one ofclaims 1 to 6, characterized in that only the tangential junction zoneof the thread root with the load flank (21, 22) is a multiple radiuszone.
 8. A threaded tubular element according to any one of claims 1 to6, characterized in that each of the two tangential junction zones ofthe thread root is a multiple radius zone.
 9. A threaded tubular elementaccording to claim 8, characterized in that the radius (r_(P1), r_(P2))of the principal arc (23, 24) of the multiple radius zone on the loadflank side is greater than or equal to that (r_(P3), r_(P4)) of theprincipal arc (53, 54) of the multiple radius zone on the stabbing flankside.
 10. A threaded tubular element according to any one of claims 1 to9, characterized in that the angle (A, B) which each of the flanks makeswith the normal to the axis of the threaded element is positive or zero.11. A threaded tubular connection (100, 300) with a high resistance tostatic and dynamic stresses, comprising a male threaded tubular element(1) at the end of a first pipe (101, 301) connected by screwing to afemale threaded tubular element (2) at the end of a second pipe (102,302) by means of a male threading (3, 303, 303′) on the male threadedtubular element and a female threading (4, 304, 304′) on the femalethreaded tubular element, the threads (11, 12) of each of the male andfemale threadings comprising a thread crest (17, 20, S1, S2), a threadroot (18, 19, F1, F2), a rectilinear load flank (13, 14), a rectilinearstabbing flank (15, 16) and four junction zones each comprising a circleof an arc, two of these zones, the tangential thread root junction zones(21, 22, 51, 52), each joining the thread root to one flank and twozones, the thread crest junction zones (31, 32, 41, 42), each joiningthe thread crest to a flank, the profile and disposition of each threadcrest junction zone being adapted so as not to interfere with thetangential thread root junction zone of the mated threaded element,characterized in that at least one of the two threaded tubular elementsis a threaded element termed an anti-fatigue profile element accordingto any one of claims 1 to
 10. 12. A threaded tubular connectionaccording to claim 11, characterized in that at least one thread crestjunction zone of a threaded tubular element opposite a tangential threadroot junction zone with multiple radii of a mated threaded tubularelement with an anti-fatigue profile is a zone termed follower zone (31,32) which comprises two arcs of a circle which join tangentially to eachother, namely a principal arc (33, 34) and a secondary arc (35, 36),this latter to produce the tangential thread crest junction of thecorresponding flank and in that at the point termed the high junctionpoint (P_(RH1), P_(RH2)) of the corresponding flank where the supportcircle of the principal arc of the follower zone cuts the supportstraight line of the corresponding flank, the tangent to said circlemakes an acute angle (G, H) which is strictly negative with the supportstraight line of the flank under consideration.
 13. A threaded tubularconnection according to claim 11 or claim 12, characterized in that thetwo male and female elements of the threaded tubular connection are ofthe type defined in any one of claims 1 to
 10. 14. A threaded tubularconnection according to any one of claims 11 to 13, characterized inthat the threadings are interference threadings, the thread crest (20)of one threading (4) radially interfering with the thread root (19) ofthe mated threading (3).
 15. A threaded tubular connection according toany one of claims 11 to 13, characterized in that the two thread flanks(13, 15) of one threading (3) are in contact with or without contactpressure with the two thread flanks (14, 16) of the mated threading (4)over at least a portion of the length of the threadings (3, 4).